Traffic monitoring plays a crucial role in urban planning, transportation management, and road safety initiatives. However, existing monitoring systems often struggle to balance the need for high-resolution data acquisition and resource efficiency. This study proposes an innovative approach leveraging neuromorphic sensor technology to enhance traffic monitoring efficiency while still exhibiting robust performance when exposed to difficult conditions. Neuromorphic cameras, also called event-based cameras, with their high temporal and dynamic range and minimal memory usage, have found applications in various fields. However, despite their potential, their use in static traffic monitoring is largely unexplored. This study introduces eTraM, the first-of-its-kind fully event-based traffic monitoring dataset, to address the gap in existing research. eTraM offers 10 hr of data from diverse traffic scenarios under varying lighting and weather conditions, providing a comprehensive overview of real-world situations. Providing 2M bounding box annotations, it covers eight distinct classes of traffic participants, ranging from vehicles to pedestrians and micro-mobility. eTraM's utility has been assessed using state-of-the-art methods, including RVT, RED, and YOLOv8. The quantitative evaluation of the ability of event-based models to generalize on nighttime and unseen scenes further substantiates the compelling potential of leveraging event cameras for traffic monitoring, opening new avenues for research and application.